Schedule


The class schedule below will be updated on a weekly basis. The class will mainly follow the lecture notes below, which will be periodically updated.

Calder, Jeff. The Calculus of Variations. [pdf]. (Updated 2019-11-26)

Lecture Date Topic Notes
1 Sept 4 Introduction
2 Sept 6 Euler-Lagrange equations
3 Sept 9 Brachistochrone problem
4 Sept 11 Minimal surfaces of revolution
5 Sept 13 Isoperimetric inequality and hanging chains
6 Sept 16 Introduction to mulivariable problems
7 Sept 18 Euler-Lagrange equations revisited
8 Sept 20 Gradient descent
9 Sept 23 Accelerated gradient descent
10 Sept 25 Total variation image restoration
11 Sept 27 Primal dual/Split Bregman methods
12 Sept 30 Image Segmentation
13 Oct 2 Chan-Vese Active Contours
14 Oct 4 Ginzburg-Landau approximation
15 Oct 7 The direct method: Lower semicontinuity and coercivity
16 Oct 9 Sobolev spaces
17 Oct 11 Sobolev spaces
18 Oct 14 Sobolev spaces
19 Oct 16 Weak lower semicontinuity
20 Oct 18 Weak lower semicontinuity
21 Oct 21 Existence of minimizers
22 Oct 23 Uniqueness of minimizers
23 Oct 25 Minimal surface problems
24 Oct 28 a priori gradient estimates
25 Oct 30 a priori gradient estimates
26 Nov 1 Intro graph-based learning
27 Nov 4 Probability review
28 Nov 6 No class
29 Nov 8 Probability review
30 Nov 11 Concentration of measure
31 Nov 13 Concentration of measure
32 Nov 15 Concentration of measure
33 Nov 18 No class
34 Nov 20 Random geometric graphs
35 Nov 22 Pointwise consistency of graph Laplacians
36 Nov 25 Maximum principle methods
37 Nov 27 Variational consistency: Upper bounds
Thanksgiving (no class)
38 Dec 2 Transportation maps
39 Dec 4 Variational consistency: Lower bounds
40 Dec 6
41 Dec 9
42 Dec 11